Abstract
In this paper we explore a specific semi-classical orthogonal sequence, namely the generalized Gegenbauer orthogonal polynomials (GG) which appear in many applications such as the weighted L p mean convergence of Hermite–Fejér interpolation or the chain of harmonic oscillators in the absence of externally applied forces. First we trace back the genesis of GG underlining its links with the Jacobi orthogonal polynomials. Second we establish a differential–difference relation and the second-order differential equation satisfied by this sequence. We end by giving the fourth-order differential equation satisfied by the association (of arbitrary order) of the GG.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
